Details

sample446.0ms

Algorithm

intervals

Results

235.0ms	90×	body	1280	valid
133.0ms	68×	body	640	valid
19.0ms	68×	body	80	valid
19.0ms	19×	body	320	valid
8.0ms	11×	body	160	valid

simplify1.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	3141
3	655
2	181
1	74
0	32

prune43.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize89.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
0.5b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b	(- 3.0 (sqrt 5.0))
2.4b	(- (cos x) (cos y))

rewrite242.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
12×	`associate-r`
11×	`pow1` `add-cbrt-cube` `add-exp-log`
10×	`associate-*r/`
9×	`flip3--` `flip--`
8×	`add-cube-cbrt` `add-log-exp`
7×	`associate-l` `difference-of-squares`
6×	`sub-neg`
5×	`sqrt-prod`
4×	`distribute-rgt-in` `frac-times` `distribute-lft-in` `pow-prod-down` `prod-exp` `cbrt-unprod` `distribute-lft-out--`
2×	`times-frac` `diff-log` `associate-l/` `-commutative` `unswap-sqr`
1×	`diff-cos`

Counts

4 → 94

Calls

4 calls:

118.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
95.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
11.0ms	(- 3.0 (sqrt 5.0))
13.0ms	(- (cos x) (cos y))

series387.0ms

Counts

4 → 10

Calls

4 calls:

215.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
100.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
72.0ms	(- (cos x) (cos y))

simplify1.3s

Counts

104 → 104

Iterations

Iter	Nodes
done	5000
2	2910
1	652
0	241

prune1.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.3b

localize99.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (- (sin x) (/ (sin y) 16.0)) (sqrt (sqrt 2.0)))
0.3b	(* (* (sqrt (sqrt 2.0)) (* (- (sin x) (/ (sin y) 16.0)) (sqrt (sqrt 2.0)))) (- (sin y) (/ (sin x) 16.0)))
1.0b	(- 3.0 (sqrt 5.0))
2.4b	(- (cos x) (cos y))

rewrite388.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
15×	`pow1` `add-cbrt-cube` `associate-r` `add-exp-log`
13×	`sqrt-prod`
10×	`associate-*l/`
9×	`flip3--` `add-cube-cbrt` `flip--`
8×	`associate-*r/` `add-log-exp`
7×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `difference-of-squares`
4×	`frac-times` `sub-neg` `distribute-lft-out--`
3×	`unswap-sqr`
2×	`distribute-rgt-in` `distribute-lft-in` `times-frac` `diff-log` `*-commutative`
1×	`diff-cos`

Counts

4 → 97

Calls

4 calls:

70.0ms	(* (- (sin x) (/ (sin y) 16.0)) (sqrt (sqrt 2.0)))
299.0ms	(* (* (sqrt (sqrt 2.0)) (* (- (sin x) (/ (sin y) 16.0)) (sqrt (sqrt 2.0)))) (- (sin y) (/ (sin x) 16.0)))
6.0ms	(- 3.0 (sqrt 5.0))
6.0ms	(- (cos x) (cos y))

series493.0ms

Counts

4 → 10

Calls

4 calls:

180.0ms	(* (- (sin x) (/ (sin y) 16.0)) (sqrt (sqrt 2.0)))
209.0ms	(* (* (sqrt (sqrt 2.0)) (* (- (sin x) (/ (sin y) 16.0)) (sqrt (sqrt 2.0)))) (- (sin y) (/ (sin x) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
104.0ms	(- (cos x) (cos y))

simplify1.4s

Counts

107 → 107

Iterations

Iter	Nodes
done	5000
2	3047
1	690
0	259

prune1.3s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize100.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (sqrt 2.0)) (* (- (sin x) (/ (sin y) 16.0)) (sqrt (sqrt 2.0))))
0.3b	(* (- (sin x) (/ (sin y) 16.0)) (sqrt (sqrt 2.0)))
0.3b	(* (* (sqrt (sqrt 2.0)) (* (- (sin x) (/ (sin y) 16.0)) (sqrt (sqrt 2.0)))) (- (sin y) (/ (sin x) 16.0)))
2.4b	(- (cos x) (cos y))

rewrite563.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
21×	`sqrt-prod`
20×	`pow1` `add-cbrt-cube` `add-exp-log`
18×	`*-un-lft-identity`
16×	`associate-r` `associate-l`
12×	`associate-*l/` `add-cube-cbrt`
10×	`pow-prod-down` `prod-exp` `associate-*r/` `cbrt-unprod`
9×	`flip3--` `flip--`
6×	`add-log-exp`
5×	`difference-of-squares`
4×	`frac-times`
3×	`sub-neg` `*-commutative` `distribute-lft-out--` `unswap-sqr`
2×	`distribute-rgt-in` `distribute-lft-in` `times-frac`
1×	`diff-log` `diff-cos`

Counts

4 → 108

Calls

4 calls:

94.0ms	(* (sqrt (sqrt 2.0)) (* (- (sin x) (/ (sin y) 16.0)) (sqrt (sqrt 2.0))))
92.0ms	(* (- (sin x) (/ (sin y) 16.0)) (sqrt (sqrt 2.0)))
361.0ms	(* (* (sqrt (sqrt 2.0)) (* (- (sin x) (/ (sin y) 16.0)) (sqrt (sqrt 2.0)))) (- (sin y) (/ (sin x) 16.0)))
10.0ms	(- (cos x) (cos y))

series603.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(* (sqrt (sqrt 2.0)) (* (- (sin x) (/ (sin y) 16.0)) (sqrt (sqrt 2.0))))
166.0ms	(* (- (sin x) (/ (sin y) 16.0)) (sqrt (sqrt 2.0)))
213.0ms	(* (* (sqrt (sqrt 2.0)) (* (- (sin x) (/ (sin y) 16.0)) (sqrt (sqrt 2.0)))) (- (sin y) (/ (sin x) 16.0)))
97.0ms	(- (cos x) (cos y))

simplify1.4s

Counts

120 → 120

Iterations

Iter	Nodes
done	5000
2	2874
1	639
0	238

prune1.7s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize137.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (sqrt (sqrt 2.0)) (* (- (sin x) (/ (sin y) 16.0)) (sqrt (sqrt 2.0)))) (- (sin y) (/ (sin x) 16.0)))
0.5b	(cbrt (pow (- (cos x) (cos y)) 3))
0.6b	(pow (- (cos x) (cos y)) 3)
2.4b	(- (cos x) (cos y))

rewrite346.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
18×	`cbrt-prod`
14×	`pow1` `add-cbrt-cube` `add-exp-log`
12×	`unpow-prod-down` `cube-prod`
11×	`add-cube-cbrt`
9×	`flip3--` `flip--`
8×	`associate-l/` `associate-r/`
7×	`difference-of-squares`
6×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `distribute-lft-out--` `add-log-exp`
5×	`diff-cos`
4×	`cube-div` `frac-times`
3×	`pow-unpow` `sub-neg`
2×	`distribute-rgt-in` `cube-mult` `cbrt-div` `distribute-lft-in` `unpow3` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `times-frac` `pow1/3` `diff-log` `associate-l` `pow-exp` `*-commutative` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 111

Calls

4 calls:

297.0ms	(* (* (sqrt (sqrt 2.0)) (* (- (sin x) (/ (sin y) 16.0)) (sqrt (sqrt 2.0)))) (- (sin y) (/ (sin x) 16.0)))
25.0ms	(cbrt (pow (- (cos x) (cos y)) 3))
14.0ms	(pow (- (cos x) (cos y)) 3)
6.0ms	(- (cos x) (cos y))

series478.0ms

Counts

4 → 12

Calls

4 calls:

217.0ms	(* (* (sqrt (sqrt 2.0)) (* (- (sin x) (/ (sin y) 16.0)) (sqrt (sqrt 2.0)))) (- (sin y) (/ (sin x) 16.0)))
89.0ms	(cbrt (pow (- (cos x) (cos y)) 3))
102.0ms	(pow (- (cos x) (cos y)) 3)
69.0ms	(- (cos x) (cos y))

simplify2.3s

Counts

123 → 123

Iterations

Iter	Nodes
done	5001
2	3663
1	717
0	229

prune1.5s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.2b

regimes235.0ms

Accuracy

0% (0.2b remaining)

Error of 0.5b against oracle of 0.3b and baseline of 0.5b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	58
1	58
0	44

end0.0ms

sample15.8s

Algorithm

intervals

Results

8.0s	2681×	body	1280	valid
4.9s	1839×	body	640	valid
1.4s	2356×	body	80	valid
842.0ms	757×	body	320	valid
230.0ms	367×	body	160	valid